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NTA Abhyas 2020
Exam
NTA Abhyas
Year
2020
Subject
Physics
Chapter
Units and Dimensions

NTA Abhyas 2020 · Physics · Units and Dimensions

The velocity of water waves v may depend upon their wavelength λ ,...

The velocity of water waves vv may depend upon their wavelength λ\lambda , the density of water ρρ and the acceleration due to gravity gg. The method of dimensions gives the relation between these quantities as

Options

  1. Av2∝ρgv^{2} ∝ ρg
  2. Bv2∝gλρv^{2} ∝ g\lambdaρ
  3. Cv2∝gλv^{2} ∝ g\lambda
  4. Dv2∝g−1λ−3v^{2} ∝ g^{- 1} {λ}^{- 3}

Correct answer

C. v2∝gλv^{2} ∝ g\lambda

Step-by-step solution

Let vx=kgyλzρδ.v^{x} = kg^{y} {λ}^{z} {ρ}^{δ}. Now by substituting the dimensions of each quantities and equating the powers of M, L and T we get δ=0\delta = 0 and x=2,y=1,z=1x = 2, y = 1, z = 1.
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